Finite-dimensional irreducible representations of the Lie superalgebra sl(1,3) in a Gel’fand–Zetlin basis

Abstract

A concept of a Gel’fand–Zetlin pattern for the Lie superalgebra sl(1,3) is introduced. Within every finite-dimensional irreducible sl(1,3) module the set of the Gel’fand–Zetlin patterns constitute an orthonormed basis, called a Gel’fand–Zetlin basis. Expressions for the transformation of this basis under the action of the generators are written down for every finite-dimensional irreducible representation.